Microeconomics theory through applications

This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License without attribution as requested by the work’s original creator or licensee Saylor URL: http://www.saylor.org/books Saylor.org Preface We have written a fundamentally different text for principles of economics, based on two premises: Students are motivated to study economics if they see that it relates to their own lives Students learn best from an inductive approach, in which they are first confronted with a question and then led through the process of how to answer that question The intended audience of the textbook is first-year undergraduates taking courses on the principles of macroeconomics and microeconomics Many may never take another economics course We aim to increase their economic literacy both by developing their aptitude for economic thinking and by presenting key insights about economics that every educated individual should know Applications ahead of Theory We present all the theory that is standard in books on the principles of economics But by beginning with applications, we also show students why this theory is needed We take the kind of material that other authors put in “applications boxes” and place it at the heart of our book Each chapter is built around a particular business or policy application, such as (for microeconomics) minimum wages, stock exchanges, and auctions, and (for macroeconomics), social security, globalization, and the wealth and poverty of nations Why take this approach? Traditional courses focus too much on abstract theory relative to the interests and capabilities of the average undergraduate Students are rarely engaged, and the formal theory is never integrated into the way students think about economic issues We provide students with a vehicle to understand the structure of economics, and we train them how to use this structure A New Organization Traditional books are organized around theoretical constructs that mean nothing to students Our book is organized around the use of economics Saylor URL: http://www.saylor.org/books Saylor.org Our applications-first approach leads to a fundamental reorganization of the textbook Students will not see chapters with titles like “Cost Functions” or “Short-Run Fluctuations.” We introduce tools and ideas as, and when, they are needed Each chapter is designed with two goals First, the application upon which the chapter is built provides a “hook” that gets students’ attention Second, the application is a suitable vehicle for teaching the principles of economics Learning through Repetition Important tools appear over and over again, allowing students to learn from repetition and to see how one framework can be useful in many different contexts Each piece of economic theory is first introduced and explained in the context of a specific application Most are reused in other chapters, so students see them in action on multiple occasions As students progress through the book, they accumulate a set of techniques and ideas These are collected separately in a “toolkit” that provides students with an easy reference and also gives them a condensed summary of economic principles for exam preparation A Truly International Book International economics is not an afterthought in our book; it is integrated throughout Many other texts pay lip service to international content We have taught in numerous countries in Europe, North America, and Asia, and we use that expertise to write a book that deals with economics in a globalized world Rigor without Fear We hold ourselves to high standards of rigor yet use mathematical argument only when it is truly necessary We believe students are capable of grasping rigorous argument, and indeed are often confused by loose argumentation But rigor need not mean high mathematical difficulty Many students—even very bright ones—switch off when they see a lot of mathematics Our book is more rigorous yet less overtly Saylor URL: http://www.saylor.org/books Saylor.org mathematical than most others in the market We also include a math/stat toolkit to help students understand the key mathematical tools they need A Textbook for the 21st Century We introduce students to accessible versions of dynamic decision-making, choice under uncertainty, and market power from the beginning Students are aware that they live in an uncertain world, and their choices are made in a forward-looking manner Yet traditional texts emphasize static choices in a world of certainty Students are also aware that firms typically set prices and that most firms sell products that are differentiated from those of their competitors Traditional texts base most of their analysis on competitive markets Students end up thinking that economic theory is unrealistic and unrelated to the real world We not shy away from dynamics and uncertainty, but instead introduce students to the tools of discounted present value and decision-making under uncertainty We also place relatively more emphasis on imperfect competition and price-setting behavior, and then explain why the competitive model is relevant even when markets are not truly competitive We give more prominence than other texts to topics such as basic game theory, statistics, auctions, and asset prices Far from being too difficult for principles students, such ideas are in fact more intuitive, relevant, and easier to understand than many traditional topics At the same time, we downplay some material that is traditionally included in principles textbooks but that can seem confusing or irrelevant to students We discuss imperfect competition in terms of market power and strategic behavior, and say little about the confusing taxonomy of market structure We present a simplified treatment of costs that—instead of giving excruciating detail about different cost definitions—explains which costs matter for which decisions, and why A Non-Ideological Book We emphasize the economics that most economists agree upon, minimizing debates and schools of thought Saylor URL: http://www.saylor.org/books Saylor.org There is probably less ideological debate today among economists than there has been for almost four decades Textbooks have not caught up We not avoid all controversy, but we avoid taking sides We choose and present our material so that instructors will have all the tools and resources they need to discuss controversial issues in the manner they choose Where appropriate, we explain why economists sometimes disagree on questions of policy Most key economic ideas—both microeconomic and macroeconomic—can be understood using basic tools of markets, accounting identities, and budget sets These are simpler for students to understand, are less controversial within the profession, and not require allegiance to a particular school of thought A Single Voice The book is a truly collaborative venture Very often, coauthored textbooks have one author for microeconomics and another for macroeconomics Both of us have researched and taught both microeconomic and macroeconomic topics, and we have worked together on all aspects of the book This means that students who study both microeconomics and macroeconomics from our book will benefit from a completely integrated and consistent approach to economics Saylor URL: http://www.saylor.org/books Saylor.org Chapter What Is Economics? Fast-Food Economics You are just beginning your study of economics, but let us fast-forward to the end of your first economics course How will your study of economics affect the way you see the world? The final exam is over You are sitting at a restaurant table, waiting for your friends to arrive The place is busy and loud as usual Looking around, you see small groups of people sitting and talking animatedly Most of the customers are young; this is not somewhere your parents visit very often At the counter, people line up to buy food You watch a woman choose some items from the menu and hand some notes and coins to the young man behind the counter He is about the same age as you, and you think that he is probably from China After a few moments, he hands her some items, and she takes them to a table next to yours Where are you? Based on this description, you could be almost anywhere in the world This particular fast-food restaurant is a Kentucky Fried Chicken, or KFC, but it could easily have been a McDonald’s, a Burger King, or any number of other fast-food chains Restaurants like this can be found in Auckland, Buenos Aires, Cairo, Denver, Edinburgh, Frankfurt, Guangzhou, and nearly every other city in the world Here, however, the menu is written in French, and the customer paid in euros (€) Welcome to Paris While you are waiting, you look around you and realize that you are not looking at the world in the same way that you previously did The final exam you just completed was for an economics course, and—for good or for ill—it has changed the way you understand the world Economics, you now understand, is all around you, all the time Saylor URL: http://www.saylor.org/books Saylor.org 1.1 Microeconomics in a Fast-Food Restaurant LEARNING OBJECTIVE What kinds of problems we study in microeconomics? You watch another customer go to the counter and place an order She purchases some fried chicken, an order of fries, and a Coca-Cola The cost is €10 She hands over a bill and gets the food in exchange It’s a simple transaction; you have witnessed exchanges like it thousands of times before Now, though, you think about the fact that this exchange has made both the customer and the store better off than they were previously The customer has voluntarily given up money to get food Presumably, she would this only if having the food makes her happier than having the €10 KFC, meanwhile, voluntarily gave up the food to get the €10 Presumably, the managers of the store would sell the food only if they benefit from the deal as well They are willing to give up something of value (their food) in exchange for something else of value (the customer’s money) Think for a moment about all the transactions that could have taken place but did not For the same €10, the customer could have bought two orders of fried chicken But she didn’t So even though you have never met the person, you know something about her You know that—at this moment at least— she prefers having a Coca-Cola, fries, and one order of fried chicken to having two orders of fried chicken You also know that she prefers having that food to any number of other things she could have bought with those euros, such as a movie theater ticket, some chocolate bars, or a book From your study of economics, you know that her decision reflects two different factors The first is her tastes Each customer likes different items on the menu Some love the spicy fried chicken; others dislike it There is no accounting for differences in tastes The second is what she can afford She has a budget in mind that limits how much she is willing to spend on fast food on a given day Her decision about what to buy comes from the interaction between her tastes and her budget Economists have built a rich and complicated theory of decision making from this basic idea You look back at the counter and to the kitchen area behind it The kitchen, you now know, is an example of a production process that takes inputs and produces output Some of the inputs are perhaps obvious, such as basic ingredients like raw chicken and cooking oil Before you took the Saylor URL: http://www.saylor.org/books Saylor.org economics course, you might have thought only about those ingredients Now you know that there are many more inputs to the production process, including the following:  The building housing the restaurant  The tables and chairs inside the room  The people working behind the cash register and in the kitchen  The people working at KFC headquarters managing the outlets in Paris  The stoves, ovens, and other equipment in the kitchen used to cook the food  The energy used to run the stoves, the ovens, the lighting, and the heat  The recipes used to convert the ingredients into a finished product The outputs of KFC are all the items listed on the menu And, you realize, the restaurant provides not only the food but also an additional service, which is a place where you can eat the food Transforming these inputs (for example, tables, chickens, people, recipes) into outputs is not easy Let us examine one output—for example, an order of fried chicken The production process starts with the purchase of some uncooked chicken A cook then adds some spices to the chicken and places it in a vat of very hot oil in the huge pots in the kitchen Once the chicken is cooked, it is placed in a box for you and served to you at the counter That production process uses, to a greater or lesser degree, almost all the inputs of KFC The person responsible for overseeing this transformation is the manager Of course, she doesn’t have to analyze how to this herself; the head office provides a detailed organizational plan to help her KFC management decides not only what to produce and how to produce it but also how much to charge for each item Before you took your economics course, you probably gave very little thought to where those prices on the menu came from You look at the price again: €5 for an order of fried chicken Just as you were able to learn some things about the customer from observing her decision, you realize that you can also learn something about KFC You know that KFC wouldn’t sell an order of fried chicken at that price unless it was able to make a profit by doing so For example, if a piece of raw chicken cost €6, then KFC would obviously make a loss So the price charged must be greater than the cost of producing the fried chicken Saylor URL: http://www.saylor.org/books Saylor.org KFC can’t set the price too low, or it would lose money It also can’t set the price too high What would happen if KFC tried to charge, say, €100 for an order of chicken? Common sense tells you that no one would buy it at that price Now you understand that the challenge of pricing is to find a balance: KFC needs to set the price high enough to earn a good profit on each order sold but not so high that it drives away too many customers In general, there is a trade-off: as the price increases, each piece sold brings in more revenue, but fewer pieces are sold Managers need to understand this trade-off between price and quantity, which economists call demand It depends on many things, most of which are beyond the manager’s control These include the income of potential customers, the prices charged in alternative restaurants nearby, the number of people who think that going to KFC is a cool thing to do, and so on The simple transaction between the customer and the restaurant was therefore the outcome of many economic choices You can see other examples of economics as you look around you—for example, you might know that the workers earn relatively low wages; indeed, they may very well be earning minimum wage Across the street, however, you see a very different kind of establishment: a fancy restaurant The chef there is also preparing food for customers, but he undoubtedly earns a much higher wage than KFC cooks Before studying economics, you would have found it hard to explain why two cooks should earn such different amounts Now you notice that most of the workers at KFC are young—possibly students trying to earn a few euros a month to help support them through college They not have years of experience, and they have not spent years studying the art of cooking The chef across the street, however, has chosen to invest years of his life training and acquiring specialized skills and, as a result, earns a much higher wage The well-heeled customers leaving that restaurant are likewise much richer than those around you at KFC You could probably eat for a week at KFC for the price of one meal at that restaurant Again, you used to be puzzled about why there are such disparities of income and wealth in society—why some people can afford to pay €200 for one meal while others can barely afford the prices at KFC Your study of economics has revealed that there are many causes: some people are rich because, like Saylor URL: http://www.saylor.org/books Saylor.org the skilled chef, they have abilities, education, and experience that allow them to command high wages Others are rich because of luck, such as those born of wealthy parents Everything we have discussed in this section—the production process, pricing decisions, purchase decisions, and the employment and career choices of firms and workers—are examples of what we study in the part of economics called microeconomics Microeconomics is about the behavior of individuals and firms It is also about how these individuals and firms interact with each other through markets, as they when KFC hires a worker or when a customer buys a piece of fried chicken When you sit in a fast-food restaurant and look around you, you can see microeconomic decisions everywhere KEY TAKEAWAY  In microeconomics, we study the decisions of individual entities, such as households and firms We also study how households and firms interact with each other CHECKING YOUR UNDERSTANDING List three microeconomic decisions you have made today Saylor URL: http://www.saylor.org/books Saylor.org 10 Figure 17.16 Labor Input in the Production Function The Main Uses of This Tool  Chapter "eBay and craigslist"  Chapter "Growing Jobs"  Chapter 15 "A Healthy Economy" Saylor URL: http://www.saylor.org/books Saylor.org 814 17.18 Nash Equilibrium A Nash equilibrium is used to predict the outcome of a game By a game, we mean the interaction of a few individuals, called players Each player chooses anaction and receives a payoff that depends on the actions chosen by everyone in the game A Nash equilibrium is an action for each player that satisfies two conditions: The action yields the highest payoff for that player given her predictions about the other players’ actions The player’s predictions of others’ actions are correct Thus a Nash equilibrium has two dimensions Players make decisions that are in their own self-interest, and players make accurate predictions about the actions of others Consider the games in Table 17.6 "Prisoners’ Dilemma", Table 17.7 "Dictator Game", Table 17.8 "Ultimatum Game", and Table 17.9 "Coordination Game" The numbers in the tables give the payoff to each player from the actions that can be taken, with the payoff of the row player listed first Table 17.6 Prisoners’ Dilemma Left Right Up 5, 0, 10 Down 10, 2, Table 17.7 Dictator Game Number of Dollars (x) 100 − x, x Table 17.8 Ultimatum Game Accept Reject Number of Dollars (x) 100 − x, x 0, Table 17.9 Coordination Game Left Right Saylor URL: http://www.saylor.org/books Saylor.org 815 Left Right Up 5, 0, Down 1, 4,  Prisoners’ dilemma The row player chooses between the action labeled “Up” and the one labeled “Down.” The column player chooses between the action labeled “Left” and the one labeled “Right.” For example, if row chooses “Up” and column chooses “Right,” then the row player has a payoff of 0, and the column player has a payoff of 10 If the row player predicts that the column player will choose “Left,” then the row player should choose “Down” (that is, down for the row player is her best response to left by the column player) From the column player’s perspective, if he predicts that the row player will choose “Up,” then the column player should choose “Right.” The Nash equilibrium occurs when the row player chooses “Down” and the column player chooses “Right.” Our two conditions for a Nash equilibrium of making optimal choices and predictions being right both hold  Social dilemma This is a version of the prisoners’ dilemma in which there are a large number of players, all of whom face the same payoffs  Dictator game The row player is called the dictator She is given $100 and is asked to choose how many dollars (x) to give to the column player Then the game ends Because the column player does not move in this game, the dictator game is simple to analyze: if the dictator is interested in maximizing her payoff, she should offer nothing (x = 0)  Ultimatum game This is like the dictator game except there is a second stage In the first stage, the row player is given $100 and told to choose how much to give to the column player In the second stage, the column player accepts or rejects the offer If the column player rejects the offer, neither player receives any money The best choice of the row player is then to offer a penny (the smallest amount of money there is) The best choice of the column player is to accept This is the Nash equilibrium  Coordination game The coordination game has two Nash equilibria If the column player plays “Left,” then the row player plays “Up”; if the row player plays “Up,” then the column player Saylor URL: http://www.saylor.org/books Saylor.org 816 plays “Left.” This is an equilibrium But “Down/Right” is also a Nash equilibrium Both players prefer “Up/Left,” but it is possible to get stuck in a bad equilibrium Key Insights  A Nash equilibrium is used to predict the outcome of games  In real life, payoffs may be more complicated than these games suggest Players may be motivated by fairness or spite The Main Uses of This Tool  Chapter 12 "Superstars"  Chapter 13 "Cleaning Up the Air and Using Up the Oil"  Chapter 14 "Busting Up Monopolies"  Chapter 16 "Cars" Saylor URL: http://www.saylor.org/books Saylor.org 817 17.19 Externalities and Public Goods Some economic transactions have effects on individuals not directly involved in that transaction When this happens, we say there is an externality present An externality is generated by a decision maker who disregards the effects of his actions on others In the case of a positive externality, the individual’s actions increase the welfare of others (for example, research and development by firms) In the case of a negative externality, an individual’s actions decrease the welfare of others (for example, pollution) Economic outcomes are not efficient when externalities are present So the government may be able to improve on the private outcome The possible remedies are as follows:  Subsidies (in the case of positive externalities) and taxes (in the case of negative externalities)  The creation of markets by the government If people are altruistic, then they may instead take into account others’ welfare and may internalize some of the effects of their actions We typically see externalities associated with nonexcludable goods (or resources)—goods for which it is impossible to selectively deny access In other words, it is not possible to let some people consume the good while preventing others from consuming it An excludable good (or resource) is one to which we can selectively allow or deny access If a good is nonexcludable or partially excludable, there are positive externalities associated with its production and negative externalities associated with its consumption We say that a good is a rival if one person’s consumption of the good prevents others from consuming the good Most of the goods we deal with in economics are rival goods A good is nonrival if one person can consume the good without preventing others from consuming the same good Knowledge is a nonrival good If a good is both nonexcludable and nonrival, it is a public good Key Insights  When externalities are present, the outcome is inefficient  The market will typically not provide public goods The Main Uses of This Tool Saylor URL: http://www.saylor.org/books Saylor.org 818  Chapter 11 "Barriers to Trade and the Underground Economy"  Chapter 13 "Cleaning Up the Air and Using Up the Oil"  Chapter 15 "A Healthy Economy"  Chapter 16 "Cars" Saylor URL: http://www.saylor.org/books Saylor.org 819 17.20 Foreign Exchange Market A foreign exchange market is where one currency is traded for another There is a demand for each currency and a supply of each currency In these markets, one currency is bought using another The price of one currency in terms of another (for example, how many dollars it costs to buy one Mexican peso) is called the exchange rate Foreign currencies are demanded by domestic households, firms, and governments who wish to purchase goods, services, or financial assets that are denominated in the currency of another economy For example, if a US auto importer wants to buy a German car, it must buy euros The law of demand holds: as the price of a foreign currency increases, the quantity of that currency demanded will decrease Foreign currencies are supplied by foreign households, firms, and governments that wish to purchase goods, services, or financial assets denominated in the domestic currency For example, if a Canadian bank wants to buy a US government bond, it must sell Canadian dollars As the price of a foreign currency increases, the quantity supplied of that currency increases Exchange rates are determined just like other prices: by the interaction of supply and demand At the equilibrium exchange rate, the supply and demand for a currency are equal Shifts in the supply or demand for a currency lead to changes in the exchange rate Because one currency is exchanged for another in a foreign exchange market, the demand for one currency entails the supply of another Thus the dollar market for euros (where the price is dollars per euro and the quantity is euros) is the mirror image of the euro market for dollars (where the price is euros per dollar and the quantity is dollars) To be concrete, consider the demand for and supply of euros The supply of euros comes from the following:  European households and firms that wish to buy goods and services from non-euro countries  European investors who wish to buy assets (government debt, stocks, bonds, etc.) that are denominated in currencies other than the euro The demand for euros comes from the following:  Households and firms in non-euro countries that wish to buy goods and services from Europe Saylor URL: http://www.saylor.org/books Saylor.org 820  Investors in non-euro countries that wish to buy assets (government debt, stocks, bonds, etc.) that are denominated in euros Figure 17.17 "The Foreign Exchange Market" shows the dollar market for euros On the horizontal axis is the quantity of euros traded On the vertical axis is the price in terms of dollars The intersection of the supply and demand curves determines the equilibrium exchange rate Figure 17.17 The Foreign Exchange Market The foreign exchange market can be used as a basis for comparative statics exercises We can study how changes in an economy affect the exchange rate For example, suppose there is an increase in the level of Saylor URL: http://www.saylor.org/books Saylor.org 821 economic activity in the United States This will lead to an increase in the demand for European goods and services To make these purchases, US households and firms will demand more euros This will cause an outward shift in the demand curve and an increase in the dollar price of euros When the dollar price of a euro increases, we say that the dollar has depreciated relative to the euro From the perspective of the euro, the depreciation of the dollar represents an appreciation of the euro Key Insights  As the exchange rate increases (so a currency becomes more valuable), a greater quantity of the currency is supplied to the market and a smaller quantity is demanded The Main Uses of This Tool  Chapter "Why Do Prices Change?"  Chapter "Making and Losing Money on Wall Street" Saylor URL: http://www.saylor.org/books Saylor.org 822 17.21 Percentage Changes and Growth Rates If some variable x (say, the number of gallons of gasoline sold in a week) changes from x1 to x2, then we can simply define the change in that variable as Δx = x2 −x1 But there are problems with this simple definition The number that we calculate will change depending on the units in which we measure x If we measure in millions of gallons, x will be a much smaller number than if we measure in gallons If we measured x in liters rather than gallons (as it is indeed measured in most countries), it would be a bigger number So the number we calculate depends on the units we choose To avoid these problems, we look at percentage changes and express the change as a fraction of the individual value In what follows, we use the notation %Δx to mean the percentage change in x, and we define it as follows: %Δx = (x2 − x1)/x1 A percentage change equal to 0.1 means that gasoline consumption increased by 10 percent Why? Because 10 percent means 10 “per hundred,” so 10 percent 10/100 = 0.1 Very often in economics, we are interested in changes that take place over time Thus we might want to compare gross domestic product (a measure of how much our economy has produced) between 2012 and 2013 Suppose we know that gross domestic product in the United States in 2012 was $14 trillion and that gross domestic product in 2013 was $14.7 trillion Using the letter Y to denote gross domestic product measured in trillions, we write: Y2012 = 14.0 and Y2013 = 14.7 If we want to talk about gross domestic product at different points in time without specifying a particular year, we use the notation Yt We express the change in a variable over time in the form of a growth rate, which is just an example of a percentage change Thus the growth rate of gross domestic product in 2013 is calculated as %Δ Y2013 = (Y2013 − Y2012)/ Y20126 = (14.7 − 14)/14 = 0.05 The growth rate equals percent In general, we write %Δ Yt+1 = (Yt+1 − Yt)/ Yt The Main Uses of This Tool  Chapter "Making and Losing Money on Wall Street"  Chapter 12 "Superstars" Saylor URL: http://www.saylor.org/books Saylor.org 823 17.22 Mean and Variance To start our presentation of descriptive statistics, we construct a data set using a spreadsheet program The idea is to simulate the flipping of a two-sided coin While you might think it would be easier just to flip a coin, doing this on a spreadsheet gives you a full range of tools embedded in that program To generate the data set, we drew 10 random numbers using the spreadsheet program In the program we used, the function was called RAND, and this generated the choice of a number between zero and one Those choices are listed in the second column of the table The third column creates the two events of heads and tails that we normally associate with a coin flip To generate this last column, we adopted a rule: if the random number was less than 0.5, we termed this a “tail” and assigned a to the draw; otherwise, we termed it a “head” and assigned a to the draw The choice of 0.5 as the cut-off for heads reflects the fact that we are considering the flips of a fair coin in which each side has the same probability of 0.5 Table 17.10 Draw Random Number Heads (1) or Tails (0) 0.94 0.84 0.26 0.04 0.01 0.57 0.74 0.81 0.64 Saylor URL: http://www.saylor.org/books Saylor.org 824 Draw Random Number Heads (1) or Tails (0) 10 0.25 Keep in mind that the realization of the random number in draw i is independent of the realizations of the random numbers in both past and future draws Whether a coin comes up heads or tails on any particular flip does not depend on other outcomes There are many ways to summarize the information contained in a sample of data Even before you start to compute some complicated statistics, having a way to present the data is important One possibility is a bar graph in which the fraction of observations of each outcome is easily shown Alternatively, a pie chart is often used to display this fraction Both the pie chart and bar diagram are commonly found in spreadsheet programs Economists and statisticians often want to describe data in terms of numbers rather than figures We use the data from Table 17.10 to define and illustrate two statistics that are commonly used in economics discussions The first is the mean (or average) and is a measure of central tendency Before you read any further, ask yourself what you think the average ought to be from the coin-flipping exercise It is natural to say 0.5, since half of the time the outcome will be a head and thus have a value of zero, while the remainder of the time the outcome will be a tail and thus have a value of one Whether or not that guess holds can be checked by looking at Table 17.10 and calculating the mean of the outcome We let ki be the outcome of draw i For example, from the table, k1 = and k5 = Then the formula for the mean if there are N draws is μ = Σi ki/N Here Σi ki means the sum of the ki outcomes In words, the mean, denoted by μ, is calculated by summing the draws and dividing by the number of draws, N In the table, N = 10 and the sum of the draws of random numbers is about 51.0 Thus the mean of the 10 draws is about 0.51 We can also calculate the mean of the heads/tails column, and this is 0.6, since heads came up times in our experiment This calculation of the mean differs from the mean of the draws because the numbers in the two columns differ, with the third column being a very discrete way to represent the information in the second column Saylor URL: http://www.saylor.org/books Saylor.org 825 A second commonly used statistic is a measure of dispersion of the data called the variance The variance, denoted σ2, is calculated as σ2 = Σi (ki − μ)2/(N − 1) From this formula, if all the draws were the same (thus equal to the mean), then the variance would be zero As the draws spread out from the mean (both above and below), the variance increases Since some observations are above the mean and others below, we square the difference between a single observation (ki) and the mean (μ) when calculating the variance This means that values above and below the mean both contribute a positive amount to the variance Squaring also means that values that are a long way away from the mean have a big effect on the variance For the data given in Table 17.10, the mean of the 10 draws was given: μ = 0.51 So to calculate the variance, we would subtract the mean from each draw, square the difference, and then sum up the squared differences This yields a variance of 0.118 for this draw A closely related concept is that of the standard deviation, which is just the square root of the variance For our example, the standard deviation is 0.34 The standard deviation is bigger than the variance because the variance is less than 17.23 Correlation and Causality Correlation is a statistical measure describing how two variables move together In contrast, causality (or causation) goes deeper into the relationship between two variables by looking for cause and effect Correlation is a statistical property that summarizes the way in which two variables move either over time or across people (firms, governments, etc.) The concept of correlation is quite natural to us, as we often take note of how two variables interrelate If you think back to high school, you probably have a sense of how your classmates did in terms of two measures of performance: grade point average (GPA) and results on a standardized college entrance exam (SAT) It is likely that classmates with high GPAs also had high scores on the SAT exam In this instance, we would say that the GPA and SAT scores were positively correlated: looking across your classmates, when a person’s GPA score is higher than average, that person’s SAT score is likely to be higher than average as well Saylor URL: http://www.saylor.org/books Saylor.org 826 As another example, consider the relationship between a household’s income and its expenditures on housing If you conducted a survey across households, it is likely that you would find that richer households spend more on most goods and services, including housing In this case, we would conclude that income and expenditures on housing are positively correlated When economists look at data for the whole economy, they often focus on a measure of how much is produced, which we call real gross domestic product (GDP), and the fraction of workers without jobs, called the unemployment rate Over long periods of time, when GDP is above average (so that the economy is doing well), the unemployment rate is below average In this case, GDP and the unemployment rate are negatively correlated, as they tend to move in opposite directions The fact that one variable is correlated with another does not inform us about whether one variable causes the other Imagine yourself on an airplane in a relaxed mood, reading or listening to music Suddenly, the pilot comes on the public address system and requests that you buckle your seat belt Usually, such a request is followed by turbulence This is a correlation: the announcement by the pilot is positively correlated with air turbulence The correlation is, of course, not perfect, because sometime you hit some bumps without warning and sometimes the pilot’s announcement is not followed by turbulence But—obviously!—this doesn’t mean that we could solve the turbulence problem by turning off the public address system The pilot’s announcement does notcause the turbulence The turbulence is there whether the pilot announces it or not In fact, the causality runs the other way The turbulence causes the pilot’s announcement We noted earlier that real GDP and unemployment are negatively correlated When real GDP is below average, as it is during a recession, the unemployment rate is typically above average But what is the causality here? If unemployment caused recessions, we might be tempted to adopt a policy that makes unemployment illegal For example, the government could fine firms if they lay off workers This is not a good policy because we don’t think that low unemployment causes high real GDP But nor we necessarily think that high real GDP causes low unemployment Instead, based on economic theory, we think there are other influences that affect both real GDP and unemployment Saylor URL: http://www.saylor.org/books Saylor.org 827 More Formally Suppose that you have N observations of two variables, x and y, where xi and yiare the values of these variables in observation I = 1,2, ,N The mean of x, μx, is the sum over the values of x in the sample divided by N, and likewise for y μx=x1+x2+ +xN;μy=y1+y2+ +yN/N We can also calculate the variance and standard deviations of x and y The calculation for the variance of x, denoted σ2x is σ2x=(x1−μx)+(x2−μx)+ (xN−μx)/N The standard deviation of x is the square root of σ2x, σx=√(x1−μx)2+(x2−μx)2+ (xN−μx)2/N With these ingredients, the correlation of (x,y), denoted corr(x,y), is given by corr(x,y)=(x1−μx)(y1−μy)+(x2−μx)(y2−μy)+ (xN−μx)(yN−μy)/Nσxσy The Main Uses of This Tool  Chapter 12 "Superstars" Saylor URL: http://www.saylor.org/books Saylor.org 828 ... should know Applications ahead of Theory We present all the theory that is standard in books on the principles of economics But by beginning with applications, we also show students why this theory. .. story about microeconomics How you know that it is about microeconomics? Saylor URL: http://www.saylor.org/books Saylor.org 17 Chapter Microeconomics in Action 2.1 Four Examples of Microeconomics. .. of economics called microeconomics Microeconomics is about the behavior of individuals and firms It is also about how these individuals and firms interact with each other through markets, as